| 1. |
- Beilina, Larisa, 1970
(författare)
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Energy estimates and numerical verification of the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell's system
- 2013
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Ingår i: Central European Journal of Mathematics. - : Walter de Gruyter GmbH. - 1895-1074 .- 1644-3616. ; 11:4, s. 702-733
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Tidskriftsartikel (refereegranskat)abstract
- We rigorously derive energy estimates for the second order vector wave equation with gauge condition for the electric field with non-constant electric permittivity function. This equation is used in the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell's system. Our numerical experiments illustrate efficiency of the modified hybrid scheme in two and three space dimensions when the method is applied for generation of backscattering data in the reconstruction of the electric permittivity function.
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| 2. |
- Koshev, N., et al.
(författare)
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An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data
- 2013
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Ingår i: Central European Journal of Mathematics. - : Walter de Gruyter GmbH. - 1895-1074 .- 1644-3616. ; 11:8, s. 1489-1509
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Tidskriftsartikel (refereegranskat)abstract
- We propose an adaptive finite element method for the solution of a linear Fredholm integral equation of the first kind. We derive a posteriori error estimates in the functional to be minimized and in the regularized solution to this functional, and formulate corresponding adaptive algorithms. To do this we specify nonlinear results obtained earlier for the case of a linear bounded operator. Numerical experiments justify the efficiency of our a posteriori estimates applied both to the computationally simulated and experimental backscattered data measured in microtomography.
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| 3. |
- Melgaard, Michael
(författare)
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Scattering properties for a pair of Schrödinger type operators on cylindrical domains
- 2007
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Ingår i: Central European Journal of Mathematics. - : Walter de Gruyter GmbH. - 1895-1074 .- 1644-3616. ; 5:1, s. 134-153
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Tidskriftsartikel (refereegranskat)abstract
- Strong asymptotic completeness is shown for a pair of Schrodinger type operators on a cylindrical Lipschitz domain. A key ingredient is a limiting absorption principle valid in a scale of weighted (local) Sobolev spaces with respect to the uniform topology. The results are based on a refined version of Mourre's method within the context of pseudo-selfadjoint operators.
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| 4. |
- Nagy, Károly, et al.
(författare)
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Walsh-Marcinkiewicz means and Hardy spaces
- 2014
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Ingår i: Central European Journal of Mathematics. - : Walter de Gruyter GmbH. - 1895-1074 .- 1644-3616. ; 12:8, s. 1214-1228
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Tidskriftsartikel (refereegranskat)abstract
- The main aim of this paper is to investigate the Walsh-Marcinkiewicz means on the Hardy space Hp, when 0 < p < 2/3. We define a weighted maximal operator of Walsh-Marcinkiewicz means and establish some of its properties. With its aid we provide a necessary and sufficient condition for convergence of the Walsh-Marcinkiewicz means in terms of modulus of continuity on the Hardy space Hp, and prove a strong convergence theorem for the Walsh-Marcinkiewicz means
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